Nvidia Quadro T600

Just to kick-start this: T5500 has PCIe version 2.0,
NVidia T600 was designed for PCIe 3.0 standard.

It might be compatible as normally PCIe devices are developed with backward compatibility in mind (like there are reports what it works on x4 PCIe instead of x16) but there's no warranties, it might not work (even your BIOS or hardware might not accept it). Dell doesn't list this card as recommended.

Another consideration is about drivers, T5500 is a bit old system and you might find what NVidia doesn't provide drivers for Win7/Win8 for this card (although some vendors actually do).

On a bright side there are reports what PCIe Gen3 cards do work without issues on T5500, e.g. RTX 2070 and even Gen4 RTX 3070 (not forgetting what not all PCIe slots are wired as x16 lanes),
therefore most likely T5500 should be just fine to handle NVidia T400/T600/T1000 cards (they are low-power {50W} and not requiring additional connector)

Yes it will be fine. I have used a T400 in a Precision T3610. They aren't powerful cards, but they have the Nvenc encoder so you can use it for exporting videos. It will also speed up scrubbing, but you would benefit from a more powerful graphics card. If you have a 6 or 8 pin power connector, look into more powerful GPUs